A quantum related-key attack based on the Bernstein–Vazirani algorithm

Abstract

Due to the powerful computing capability of quantum computers, cryptographic researchers have applied quantum algorithms to cryptanalysis and obtained many interesting results in recent years. In this paper, we study related-key attack in the quantum setting and propose a specific related-key attack, which can recover the key of block ciphers efficiently as long as the attacked block ciphers satisfy certain condition. The attack algorithm employs the Bernstein–Vazirani algorithm as a subroutine and requires the attacker to query the encryption oracle with quantum superpositions. We give a condition under which the attack will succeed and prove that any block cipher either satisfies the condition or has a distinguishing attack. As a specific example of its application, we use the attack algorithm to extract the private key of the Even–Mansour cipher. The results of this study show the power of related-key attack when combined with quantum algorithms and provide guidance for the design of quantum-secure block ciphers.